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< 2020 >
July
  • 07
    July 7, 2020

    Decay estimates and complete Bakry-Emry theory

    10:00 AM-11:00 AM
    July 7, 2020

    The connection between decay estimates for entropy and logarithmic Sobolev inequalities is well-established for dynamical systems on commutative systems. I will explain how to extend this to matrix-valued functions, and then apply these techniques to Lindbladians on quantum systems interacting with an environment. In fact, some Lindbladian on small quantum systems seems to contain all the relevant information of dynamical systems on groups. This is joint work with Haojian Li and Nick LaRacuente.

    Zoom: https://harvard.zoom.us/j/779283357

  • 07
    July 7, 2020

    CMSA Geometry and Physics Seminar: Collective integrable systems and global action-angle coordinates

    9:30 AM-10:30 AM
    July 7, 2020

    A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates. Moreover, the image of the moment map is a (non-simple) convex polytope.

    Zoom: https://harvard.zoom.us/j/94717938264

  • 09
    July 9, 2020

    CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality-I

    9:00 AM-10:30 AM
    July 9, 2020

    A number of strongly correlated electronic materials exhibit quantum criticality that does not fit into the conventional Landau-Ginzburg-Wilson paradigm of continuous phase transitions. Inspired by these experimental examples, I will discuss a new class of quantum phase transitions that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and electrical insulators without Fermi surface of neutral excitations. Such phase transitions are described in terms of a finite density of fractionalized excitations coupled to emergent gauge fields. I will discuss various concrete examples of such gauge theories and describe their associated phase transitions using a renormalization group framework.  Remarkably, we find examples of continuous phase transitions between Landau Fermi liquid metals and insulators, where the quantum critical point hosts a non-Fermi liquid with a sharp Fermi surface but no long-lived quasiparticles. I will comment on the relevance of this new theoretical framework for some of the most pressing questions in the field of quantum matter.

    Zoom: https://harvard.zoom.us/j/977347126

  • 13
    July 13, 2020

    CMSA Social Science Applications Forum: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls

    10:00 AM-11:00 AM
    July 13, 2020

    This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.

    For security reasons, you will have to show your full name to join the meeting.

    Zoom: https://harvard.zoom.us/j/95475021655

  • 13
    July 13, 2020

    CMSA Geometry and Physics Seminar: Berry phase in quantum field theory

    9:00 PM-10:00 PM
    July 13, 2020

    We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in (2+1)d.

    Zoom: https://harvard.zoom.us/j/94717938264